Hi,
this is quite strange. One thing that I can advice is to replace all error_reporting(0) to error_reporting(E_ALL) in the installation php files. You can just use total commander to edit that file directly from the com_joomlawatch.zip archive. Just open the install.joomlawatch.php, change the error value to E_ALL and save it. Total commander should re-pack the whole archive. Just then, try to install this modified archive.
Also make sure that your PHP settings show some errors. It's configured in the php.ini file.
We have to see the errors first to figure out what went wrong there.